`#tnvt`
`a)\frac{1}{\sqrt{x}+1}+\frac{1}{\sqrt{x}-1}+1(x>=0,x\ne1)`
`=\frac{\sqrt{x}-1+\sqrt{x}+1+x-1}{(\sqrt{x}-1)(\sqrt{x}+1)}`
`=\frac{x+2\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}`
`=\frac{(\sqrt{x}+1)^2}{(\sqrt{x}-1)(\sqrt{x}+1)}`
`=\frac{\sqrt{x}+1}{\sqrt{x}-1}`
`b)\frac{2}{\sqrt{x}+\sqrt{y}}+\frac{1}{\sqrt{x}-\sqrt{y}}+\frac{3\sqrt{x}}{y-x}(x\ney,x>=0,y>=0)`
`=\frac{2(\sqrt{x}-\sqrt{y})+\sqrt{x}+\sqrt{y}-3\sqrt{x}}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y])}`
`=\frac{2\sqrt{x}-2\sqrt{y}+\sqrt{x}+\sqrt{y}-3\sqrt{x}}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y])}`
`=\frac{-\sqrt{y}}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y])}`
`c)\frac{1}{\sqrt{x}+2}-\frac{2}{\sqrt{x}-2}+\frac{\sqrt{x}}{x-4}(x>=0,x\ne4)`
`=\frac{\sqrt{x}-2-2(\sqrt{x}+2)+\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)}`
`=\frac{\sqrt{x}-2-2\sqrt{x}-4+\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)}`
`=\frac{-6}{(\sqrt{x}-2)(\sqrt{x}+2)}`
